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Adding up resistance in series and in parallel | NCLEX-RN | Khan Academy

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    We had talked a little bit
    about the resistance equation
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    that we got from Dr. Poiseuille.
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    And the equation looked
    a little bit like this.
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    Actually, let me
    just replace this.
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    We had 8 times eta, which
    was the viscosity of blood
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    times the length
    of a vessel divided
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    by pi times the radius of that
    vessel to the fourth power.
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    And all this put together gives
    us the resistance in a vessel.
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    So thinking about this
    a little bit more,
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    let's assume for the moment
    that the blood viscosity is not
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    going to change.
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    It certainly won't change
    from moment to moment,
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    but let's say that, in
    general, blood viscosity
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    is pretty constant.
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    Now, given that, if I want
    to change the resistance,
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    then I have two variables left.
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    I've got the length of my
    vessel and I've got the radius.
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    So if I have a vessel--
    like this-- and let's
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    say it's got a certain
    radius and length.
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    And let's say that radius is
    r, and the length is here.
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    And I apply a number.
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    Let's say the number is
    2 for the resistance.
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    Well, I have two options for
    changing that resistance.
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    If I want to increase
    the resistance,
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    I can do two things.
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    So let's say I want to
    increase that resistance.
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    And you can look at the
    equation and tell me
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    what the answer would be.
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    Two things.
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    And I'll actually draw it out.
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    So one thing would be to keep
    the radius basically the same,
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    but make it much longer.
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    Because if I make it
    longer, since the L is now,
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    let's say, twice as
    long and r is the same,
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    now my resistance
    is going to double.
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    So now we go 2 times.
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    And 2 times 2 is 4.
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    So my resistance is 4.
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    OK.
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    Option 2.
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    Let's say I don't want
    to change the length.
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    I keep the length the same.
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    Instead, I could actually
    maybe change the radius.
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    And let's say I half the radius.
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    I make it half of what it was.
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    And I actually worked out
    the math in the last one.
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    And it turned out that,
    if you half the radius--
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    in the last video, that is--
    then the resistance actually
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    is 16 times higher.
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    And you can see that because
    the resistance equals
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    r to the fourth power here.
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    So because r is to the fourth
    power when you half it,
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    it goes 16-fold.
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    And so 16 times 2 is 32.
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    So our resistance is 32.
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    So these are the two strategies,
    if you think of it that way,
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    that a blood vessel can
    use to increase resistance.
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    And of the two, you can
    see that one of them
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    is definitely more effective.
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    I mean, I can see
    that because it's
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    raised to the fourth
    power, this is
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    going to work much more
    effectively to raise
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    the resistance than
    changing the length.
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    And additionally,
    if you think of it
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    kind of from a
    practical standpoint,
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    keep in mind that I
    have smooth muscle.
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    So it's actually pretty
    easy to accomplish this--
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    or at least possible
    to accomplish this.
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    Whereas trying to
    actually change
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    the length-- which is
    option 1-- is not feasible.
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    I mean, it's much, much more
    complicated to actually expect
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    a vessel to simply
    double in its length
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    because it wants to
    raise the resistance.
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    So for multiple reasons,
    changing radius,
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    again, becomes the
    name of the game.
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    OK.
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    So let's complicate
    this a little bit.
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    Let's say instead of one
    vessel, I've got three vessels.
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    I've got, let's say,
    one vessel here.
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    And there's, let's say, 5.
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    And then I've got, let's
    see, a longer vessel here.
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    And this one happens to have
    a resistance of, let's say, 8
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    because it's longer.
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    And let's do the same radius
    for all these, but shorter now.
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    This one is 2.
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    And I want blood to flow
    through all three of these.
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    What is my total resistance?
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    And here we're talking
    about the three vessels
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    being in a series--
    meaning that you actually
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    expect the blood to
    go through all three
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    of the vessels or tubes.
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    So if they're going to go
    through all three tubes, what
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    you have to do is
    simply add up the total.
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    So resistance total-- so
    this is total resistance.
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    And I just put a
    little t to remind me
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    that that means total.
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    So total resistance equals
    the resistance of one part
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    plus the second part
    plus the third part.
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    And if you had a
    fourth or fifth part,
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    you just keep adding them up.
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    So in this case, you
    have 5, 8, and 2.
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    So Rt becomes 5 plus 8
    plus 2, and that equals 15.
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    So total resistance would be 15.
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    And actually, I'm going to
    give you a general rule.
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    Total resistance is
    always, always greater
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    than any component.
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    And you can see how
    this is very intuitive.
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    I mean, how could you possibly
    have a situation where--
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    if you're just simply
    adding them up,
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    because we don't expect
    any negative resistance
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    in this situation.
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    You're simply adding up all
    these positive resistances.
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    Of course, the total
    will be always greater
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    than any one component.
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    Seems intuitive, but I just
    wanted to spell that out.
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    So now, let's take
    a scenario where
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    you have a human body,
    a vessel in the body.
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    And let's say you have
    three parts to it,
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    and these are equal parts.
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    So let's say the resistance
    here is 2, 2, and 2.
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    Obviously, I want to calculate--
    as before-- my total.
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    So my total will be 2
    plus 2 plus 2, which is 6.
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    And then, an interesting
    thing happens.
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    So you have, let's say-- I'll
    draw the same vessel again.
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    A really interesting
    thing happens.
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    This is the same blood vessel,
    but now you have a blood clot.
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    And this blood clot is floating
    through the blood vessels.
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    And it kind of makes
    its way to this one
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    that we're working with.
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    And it goes and
    lodges right here.
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    So right here you have
    a lodged blood vessel.
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    Wow.
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    That's pretty big, but it's
    right in that middle third
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    of our vessel.
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    So we have now a tiny
    little radius here.
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    It's about, let's say,
    half of what we had before.
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    The new radius equals half
    of what the old radius was.
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    And you know from
    the last example
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    that's going to increase the
    resistance in that part by 16.
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    So the resistance
    here stays at 2.
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    Here it stays at 2.
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    But here in the middle,
    it goes from 2 to 32
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    because it's 16 times greater.
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    So you end up increasing
    the resistance
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    in the middle section by a lot.
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    So let me just write
    that out for you.
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    So 2 times 16 gets us to 32.
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    So here the resistance is 32.
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    And so if I wanted to
    calculate the total resistance,
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    I'd get something like this--
    32 plus 2 plus 2 is 36.
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    So I actually went from 6
    to 36 when this blood clot
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    came and clogged up
    part of that vessel.
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    So just keep that in mind.
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    We'll talk about that
    a little bit more,
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    but I just wanted
    to use this example
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    and also kind of
    cement the idea of what
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    you do with resistance
    in a series.
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    Let's contrast that to
    a different situation.
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    And this is when you have
    resistance in parallel.
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    So instead of asking
    blood to either kind of go
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    through all of my vessels,
    I could also do something
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    like this-- I could
    say, well, let's say,
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    I have three vessels again.
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    And this time, I'm
    going to change
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    the length and the radius.
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    And let's say this
    one's really big.
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    And the resistance here,
    let's say, is 5, here is 10,
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    and here is 6.
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    So you've got three
    different resistances.
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    And the blood now
    can choose to go
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    through any one of these paths.
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    It doesn't have to
    go through all three.
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    So how do I figure out now
    what the total resistance is?
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    So what is the total resistance?
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    Well, the total
    resistance this time
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    is going to be 1 over 1 R1,
    plus 1 over R2, plus 1 over R3.
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    And you can go on and
    on just as before.
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    But in this case,
    we only have three.
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    So let's just put that there,
    that there, and that there.
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    And I can figure this
    out pretty easily.
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    So I can say 1 over 1 over
    6 plus 1 over 10 plus 1/5.
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    And the common
    denominator there is 30.
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    So I could say 5/30.
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    This is 3/30, and
    this would be 6/30.
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    And adding that up together,
    I get 1 over 14/30 or 30
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    over 14, which is 2
    and let's say 0.1.
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    So 2.1.
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    So the total
    resistance here is 2.1.
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    Putting all three of these
    together is pretty interesting.
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    And I want you to realize
    that the resistance in total
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    is actually less than
    any component part.
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    So unlike before where we said
    that the total resistance is
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    greater than any component,
    here an interesting feature
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    is that you have
    total resistance
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    is always less
    than any component.
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    So a pretty cool set of rules
    that we can kind of go forward
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    with.
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Title:
Adding up resistance in series and in parallel | NCLEX-RN | Khan Academy
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Video Language:
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Duration:
10:33

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